Descriptive Statistics Questions and Answers

A group of twenty people played a game. The frequency distribution of their scores is: score 1 with frequency 2, score 2 with frequency 5, score 4 with frequency 7, and score $x$ with frequency 6. If the mean score is 5, what is the value of $x$?

A group of twenty people played a game with scores 1, 2, 4 and 10, having frequencies 2, 5, 7 and 6 respectively (mean score 5). What is the variance of this distribution?

The times to the nearest minute taken by 12 students to complete a task are: 43, 45, 46, 42, 48, 42, 46, 55, 47, 42, 41, 44. What is the median time, in minutes?

The times to the nearest minute taken by 12 students to complete a task are: 43, 45, 46, 42, 48, 42, 46, 55, 47, 42, 41, 44. What is the interquartile range (Q3 minus Q1) of these times, in minutes?

The times to the nearest minute taken by 12 students to complete a task are 43, 45, 46, 42, 48, 42, 46, 55, 47, 42, 41, 44, giving Q1 = 42, median = 44.5, and Q3 = 46.5 minutes (IQR = 4.5). The upper fence for outliers is Q3 + 1.5×IQR = 53.25 minutes. What can be concluded about the value 55 and the overall shape of the distribution?

A method of collecting statistical data involves obtaining information from every single member of a population, rather than from a sample of it. What is this method of data collection called?

In a survey of 100 athletes at a marathon, the amount of water taken, in litres, was recorded as: 0-0.5 litres by 8 athletes, 0.5-1.0 litres by 20 athletes, 1.0-1.5 litres by 29 athletes, 1.5-2.0 litres by 22 athletes, and 2.0-2.5 litres by 21 athletes. Using the midpoint of each class, what is the estimated mean amount of water taken, in litres?

In a survey of 100 athletes at a marathon, the amount of water taken, in litres, was recorded as: 0-0.5 litres by 8 athletes, 0.5-1.0 litres by 20 athletes, 1.0-1.5 litres by 29 athletes, 1.5-2.0 litres by 22 athletes, and 2.0-2.5 litres by 21 athletes. Using the midpoint of each class and a mean of 1.39 litres, what is the estimated standard deviation of the amount of water taken, correct to 3 decimal places?

A stem-and-leaf diagram of pocket money (in dollars) received by a group of girls is given below, with key $3|30 = \$3.30$:

Using the same pocket money data (20 girls, values in cents: 50,50,50,75,100,100,100,150,175,200,200,200,250,250,300,325,330,375,450,550, mean \$2.14), what is the standard deviation, to the nearest cent?

The table below shows the masses of 200 students measured to the nearest kg.

A group of 50 children raised money for charity. The amount raised by each child, to the nearest dollar ($), is recorded in the table.

The table shows the number of children below the age of 15 known to have suffered from measles in 2009 in a certain village.